On equivalency of zero-divisor codes via classifying their idempotent generator

Kai Lin Ong, Miin Huey Ang

Research output: Contribution to journalArticlepeer-review

Abstract

In 2009, Ted and Paul Hurley proposed a code construction method using group rings. These codes with single generator are termed group ring codes and in particular zero-divisor codes when using zero-divisors as generators. In this paper, we mainly study the equivalency of zero-divisor codes in F2G having generator from I(G), the set of all idempotents in F2G. For abelian G, our previous notion of generated idempotents completely classified I(G) by serving as its basis. Here, we first extend the notion of generated idempotents to study and classify some elements in I(G) for non-abelian G. Later, the study is generally done on equivalency of zero-divisor codes in F2G, then concentrating on those with idempotent generator. In particular, we affirm the conjecture “Every group ring code in F2D2 n is equivalent to some in F2C2 n” in the cases where the generators are our classified idempotents. We also show that the equivalency of zero-divisor codes in F2Cn with generated idempotent as generators can be established sufficiently on the generator property.

Original languageEnglish
Pages (from-to)2051-2065
Number of pages15
JournalDesigns, Codes, and Cryptography
Volume88
Issue number10
Early online date1 Jun 2020
DOIs
Publication statusPublished - Oct 2020

Keywords

  • Code equivalency
  • Group ring code
  • Idempotent
  • Zero-divisor code

ASJC Scopus subject areas

  • Computer Science Applications
  • Applied Mathematics

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